Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
SEQUENCE SPACES AND MATRIX TRANSFORMATIONS I MAT 601 0 3 + 0 3 6
Ön Koşul Dersleri Linear Functional Analysis I-II
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. METİN BAŞARIR Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı The understanding of Matrix transformations in sequence spaces, The learning of general summability theory, The understanding of classical summability methods Dersin İçeriği Matrix Transformations in sequence spaces (Matrix and Linear Transformations, Matrix Algebras, Summability, Tauberian Theorems), General Summability Theory (Main Definitions and Concepts, Silverman-Toeplitz Theorem, Invertibility, Inclusion, Translativity), Classical Summability Methods (The Nörlund Mean, Hölder and Cesaro Mean, Euler, Taylor and Borel Transformations, Hausdorff Mean)
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she recognizes sequence spaces. 1 - 2 - 3 - 14 - A - C - 2 - He/she expresses matrix transformations between sequence spaces. 1 - 2 - 3 - 14 - A - C - 3 - He/she summarizes general summability theory. 1 - 2 - 3 - 14 - A - C - 4 - He/she explains and interprets classical summability methods. 1 - 2 - 3 - 14 - A - C - 5 - He/she expresses and proves Silverman-Toeplitz theorem. 1 - 2 - 3 - 14 - A - C - 6 - He/she interprets Tauberian theorems. 1 - 2 - 3 - 14 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 14:Self Study Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Sequence Spaces
2 Matrix and Linear Transformations
3 Matrix Algebras, Summability
4 Tauberian Theorems
5 General Summability Theory
6 Silverman-Toeplitz Theorem, Invertibility
7 Inclusion, Translativity
9 Mid-Term
10 The Nörlund Mean
11 Cayley Mean
12 Hölder and Cesaro Mean
13 Euler, Taylor and Borel Transformations
14 Hausdorff Mean

#### Kaynaklar

Ders Notu [1] Musayev, Binali; Fonksiyonel Analiz, Balcı Yayınları, 2000, İstanbul
Ders Kaynakları [2] Maddox,I.J.; Elements of Functional Analysis, Cambridge Un.Press,1970,London.
[3] Şuhubi, Erdoğan; Fonksiyonel Analiz, İTÜ Vakfı, 2001, İstanbul
[4] Naylor, Arch; Linear Operator Theory in Engineering and Science, Springer-Verlag, 1982.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application.
2 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
3 Student completes the missing or limited knowledge by using the scientific methods. X
4 Student completes the missing or limited knowledge by using the scientific methods.
5 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result.
6 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
7 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
8 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field.
9 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches.
10 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
11 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
12 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity.
13 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters.
14 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
15 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
16 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work.
17 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
18 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
19 Student follows the necessary technological developments in his/her field, and s/he uses them. X
20 Student follows the necessary technological developments in his/her field, and s/he uses them.
21 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data.

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 80
Odev 1 10
Odev 2 10
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Assignment 2 10 20
Final examination 1 25 25
Toplam İş Yükü 161
Toplam İş Yükü /25(s) 6.44
Dersin AKTS Kredisi 6.44
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